Let $X$ be a topological vector space, s.t. there exists a $0$-neighbourhood (sub-)base of von Neumann-bounded subsets. Do such spaces have a name?
2026-03-31 07:53:03.1774943583
Topological vector spaces with $0$-neighbourhood base of von Neumann-bounded sets
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Such a topological vector space is called "locally bounded". Note that any subset of a bounded set is bounded, so actually it suffices for there to exist just a single bounded neighborhood of $0$.